ELSEVIER
Tectonophysics 303 (1999) 175–191
Frictional–viscous flow in mylonite with varied bimineralic
composition and its effect on lithospheric strength
M.R. Handy Ł , S.B. Wissing, L.E. Streit 1
Institut für Geowissenschaften, Universität Giessen, D-35390 Giessen, Germany
Received 1 August 1997; accepted 10 February 1998
Abstract
A theoretical, composite flow law is presented for mylonite containing interconnected layers of a weak mineral
undergoing power law creep and porphyroclasts of a stronger mineral undergoing fracture and frictional sliding. Such
mylonite, termed clastomylonite, is said to undergo frictional–viscous (FV) mylonitic flow. Its bulk strength is expressed
as a function of bimineralic composition, temperature, effective pressure, and shear strain rate, as well as the material
parameters for the constituent minerals. The FV flow law predicts that the rheology of clastomylonite is predominantly
non-linear viscous and only slightly pressure-sensitive for most bimineralic compositions. FV mylonitic flow is shown to
occupy a depth interval between cataclastic flow involving adhesive wear in the upper crust and fully viscous mylonitic
flow at greater depths. The transition from adhesive wear to FV mylonitic flow is related to the onset of dislocation creep
(glide-plus-climb) in the weakest phase and is inferred to coincide with a crustal strength maximum. A peak strength
of about 80 MPa is calculated with a combination of Byerlee’s constants for frictional sliding of granite and the FV
flow law for granitic clastomylonite (30 vol.% quartz) at elevated fluid pressures. This value falls within the range of
flow stresses independently obtained from quartz palaeopiezometry in many greenschist facies, granitic mylonite zones.
 1999 Elsevier Science B.V. All rights reserved.
Keywords: brittle–ductile transition; polyphase rheology; mylonite
1. Introduction
Mylonite or mylonitic fault rock is generally
considered to originate at crustal depths where deformation involves predominantly temperature- and
strain-rate-dependent, intracrystalline plasticity (e.g.,
Sibson, 1977; Scholz, 1990 and references therein).
Ł Corresponding
author. Fax: C49-641-99-36019; E-mail:
[email protected]
1 Present address: Dept. of Geology, Australian National University, Australia.
Yet in most mylonite, the mineral or minerals making up the matrix usually deform by one or more
thermally activated deformation mechanisms that are
associated with both non-linear (dislocation creep)
and linear (diffusion-accommodated grain-boundary sliding, pressure solution) viscous rheologies
(Schmid and Handy, 1990). Deformation involving
such mechanisms is therefore termed viscous flow.
The inclusions within the mylonitic matrix deform
either by viscous flow or cataclasis (e.g., Mitra,
1978; White et al., 1980). Handy (1990) therefore
distinguished three types of steady-state microstruc-
0040-1951/99/$ – see front matter  1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 4 0 - 1 9 5 1 ( 9 8 ) 0 0 2 5 1 - 0
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M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
Fig. 1. Sketch of the three end-member types of steady-state,
mylonitic microstructure modelled in this paper. (a) Mylonite
with both minerals deforming viscously and the strong mineral forming a load-bearing framework. (b) Mylonite with both
minerals deforming viscously and the weaker mineral forming
interconnected layers. (c) Mylonite with weak, viscous mineral
in interconnected layers and stronger porphyroclasts deforming
cataclastically. LBF D load-bearing framework; IWL D interconnected weak layers. Subscripts denote rheologies (f D frictional,
v D viscous) of the strong and weak minerals in the rock. See
text for definitions.
ture in mylonite on the basis of the shape, distribution and contrasting rheologies of their constituent
minerals. The first type is a load-bearing framework (LBF) structure (Fig. 1a), whereas the second
and third types have an interconnected weak layer
(IWL) structure containing viscous boudins (Fig. 1b,
IWLvv ) or porphyroclasts (Fig. 1c, IWLfv ). The subscripts refer to the general rheology ( f D frictional,
v D viscous) of the strong and weak minerals in the
rock.
This paper focusses on the rheology of mylonite
in which interconnected layers of a weak mineral
deform by viscous flow and porphyroclasts of a
strong mineral undergo frictional flow, i.e., cataclasis (microcracking, frictional sliding, and rigid-body
rotation), as depicted in Fig. 1c. We refer to such a
mylonite as ‘clastomylonite’, to its microstructure as
IWLfv , and to the bulk deformation of its structurally
segregated minerals as frictional–viscous or ‘FV mylonitic flow’. Because porphyroclasts undergo cataclasis and cataclasis involves dilatancy, one can predict that the bulk deformation of clastomylonite has
a dilatant component and is therefore pressure- as
well as temperature- and strain-rate-dependent. Such
mixed P-, T - and "P -dependent behaviour is often
termed ‘semi-brittle’ (Carter and Kirby, 1978) or
‘quasi-plastic’ (Sibson, 1977; Sibson, 1986) in the
rock mechanics literature. We will avoid these terms,
however, because ‘quasi-plastic’ connotes intracrystalline plasticity (Sibson, 1977) and apparently excludes other viscous flow mechanisms such as diffusion creep, whereas ‘semi-brittle’ is often also used
in a mechanistic sense to describe distributed microcracking and frictional grain-boundary sliding (cataclasis) with adhesive wear along sliding surfaces
(Scholz, 1988; Evans and Kohlstedt, 1995). Adhesive wear involves limited intracrystalline plasticity
and is inferred to occur within a specific depth-range
of the crust between fully frictional, abrasive wear
and fully viscous flow (Scholz, 1988; Scholz, 1990).
As discussed in the last part of this paper, the rheology and microstructure of a cataclasite undergoing
adhesive wear are probably quite different than those
of clastomylonite undergoing FV mylonitic flow.
In recent years, several approaches have been
developed to model heterogeneous viscous flow of
coarse-grained, polyphase rock. Tullis et al. (1991)
digitized both the microstructure of real rock and the
geometry of idealized inclusions as a basis for finite
element modelling of aggregate viscous strength. Although refined, this method is so rock-specific and
time-intensive as to be of limited practical use in
modelling lithospheric rheology. Based on their calculated finite-element rock strengths, these authors
derived a set of empirical equations expressing the
non-linear dependence of material parameters on
composition for power law creep. However, their approach is only valid when applied to rocks whose
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
constituent minerals have low viscous strength contrasts (Tullis et al., 1991). Handy (1994a) derived
composite flow laws for mylonite containing two
viscous phases and having either LBFvv , or IWLvv
microstructures (Fig. 1a,b); the IWLfv microstructure was neglected. Ji and Zhao (1993) presented
an iterative function for averaging uniform strain
rate and uniform stress estimates of viscous aggregate strength with an arbitrary number of phases.
As in older models based on similar principles (e.g.,
Voight–Hill–Reuss), the physical significance of the
averaging procedure is unclear. In another attempt, Ji
and Zhao (1994) modified elasto-plastic fibre-loading theory to obtain visco-plastic flow equations for
clastomylonitic aggregates. Unfortunately, composite strength in these equations is not an explicit function of pressure and temperature. Ivins and Sammis
(1996) adopt Maxwellian visco-elastic rheologies for
weak spherical inclusions in a strong matrix (LBFvv
structure) to model transient, composite creep of the
lower crust.
Clearly, existing models for the composite rheology of rocks simulate some, but not all of the main
features of mylonitic deformation. Either these models do not explicitly incorporate realistic mylonitic
microstructures, or they neglect the bulk rheological effects of P-dependent, brittle behaviour in one
of the mineral phases and T - and "P -dependent behaviour in the other.
In this paper, we extend the phenomenological
approach of Handy (1994a) to develop a new composite flow law for clastomylonite. We then employ
a criterion of strain energy minimization to determine the dynamic stability of the IWLfv microstructure in clastomylonite relative to that of the LBFvv
and IWLvv microstructures in mylonites whose constituent minerals undergo viscous, power law creep.
The new composite flow law is used to constrain the
compositional dependence of lithospheric strength
and to predict the strength of natural quartzofeldspathic mylonite. Various material parameters for failure and frictional sliding are substituted into the new
flow law to examine the effect of different local stress
states on the potential depth-range of porphyroclast
formation. Finally, we cast the results of our modelling in a more general context to modify current
notions on the relationship between rock structure
and lithospheric rheology.
177
2. Theory
The general approach adopted below to predict
the strength and structure of bimineralic mylonite
involves two steps (Handy, 1994a). First, we derive
flow laws for mylonite with the three steady-state
microstructures depicted in Fig. 1. We then employ
a criterion of strain energy minimization for determining which of these microstructures is stable at a
specified set of conditions.
2.1. Flow laws for fully viscous mylonites (LBFvv
and IWLvv microstructures)
Mylonite with an LBFvv microstructure has a viscously deforming framework of strong mineral containing inclusions of a weaker, viscously deforming
mineral (Fig. 1a). The strong, load-bearing framework constrains the weaker inclusions to deform at
the same rate, leading to a uniform strain rate, upper bound approximation of composite viscous shear
strength, −rLBF :
−rLBF D −wr w C −sr .1
w /
(1)
where the superscript LBF denotes the load-bearing
framework structure and the subscript r indicates the
composite rock. −wr and are −sr , the shear strengths of
the weak and strong phases. The subscripts wr and
sr indicate that the shear strengths of the constituent
phases are defined at a reference shear strain rate
equal to the shear strain rate of the entire rock (Pr ).
w is the volume proportion of weak phase in the
rock. Note that in a bimineralic rock, (1 w / D s ,
where s is the volume proportion of strong phase.
Only steady-state microstructures are considered in
this paper, so the volume proportions of both phases
remain constant with strain.
Both the weak and strong minerals are assumed
to deform solely by dislocation creep and therefore
to have rheologies that obey the empirically derived
power law for thermally activated creep (Weertman,
1968):
½¦
² P
1 Q
C ln .nC1/=2
(2)
− D exp
n RT
3
A
where − and P represent the shear strength and shear
strain rate in a mineral phase at temperature T , and
where the material constants are the activation enthalpy of creep Q, the creep exponent n, and the
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M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
pre-exponential function A. The factor 3.nC1/=2 (Nye,
1953) converts the stress and strain rate tensors of the
flattening configuration in the triaxial experiments to
the octahedral shear configuration used to approximate simple shear. We note that the stresses and
strain rates of the constituent minerals are not specified at every point within the aggregate and therefore
represent only averages of the actual heterogeneous
stresses and shear strain rates. In real rocks, both
stress and strain rate vary within the microstructure,
depending on the shape, distribution and relative
proportions of minerals with contrasting rheologies
(see fig. 6 in Handy, 1990; figs. 4 and 7 in Tullis et
al., 1991). The effects on composite rock strength of
averaging stress and strain rate are discussed on pp.
299–300 of Handy (1994a).
Mylonites with IWL structures comprise interconnected layers of weak phase that surround either
viscously deforming boudins (Fig. 1b) or brittly deforming inclusions (Fig. 1c) of a stronger phase. The
interconnectedness of the weak layers allows them
to accommodate an amount of shear strain that is
inversely and non-linearly proportional to both the
volume proportions and the viscous strength contrast
−c of the constituent minerals. The relationship between the shear strain rates of the weak and strong
phases in the rock (respectively Pw and Ps / and the
bulk shear strain rate of the rock, Pr , is (full derivation on pp. 295–296 in Handy, 1994a; see Handy,
1994b for a minor correction):
Pw D Pr w 1=−c
Ps D Pr
1
(3)
1 .1=−c /
w
(4)
1 w
The viscous strength contrast −c is defined as the
ratio −sr =−wr , where −wr and −sr are the reference shear
strengths of the weak and strong phases, as defined
above in Eq. 1. The shear strength of a mylonite with
an IWL microstructure, −rIWL , is then:
Ð
(5)
−rIWL D −w w 1=−c C −s 1 w 1=−c
where −w and −s are the shear strengths of the weak
and strong phases deforming, respectively, at the
shear strain rates Pw and Ps in Eqs. 3 and 4 for a
specified volume proportion of weak phase w .
Substituting Eq. 2 and the appropriate material
constants therein into the −wr and −sr terms in Eq. 1
allows one to calculate the shear strength of mylonite with the LBFvv microstructure. Likewise, substitution of Eq. 2 and the material constants of the
constituent minerals into the −w and −s terms in Eq. 5
allows one to calculate the shear strength of mylonite with the IWLvv microstructure. In both cases,
one must specify the volume proportion of weak
phase w , the temperature T , and the bulk rock strain
rate Pr .
2.2. Flow law for clastomylonite (IWLfv
microstructure)
Up to this point, we have followed closely
Handy’s (1994a) derivation for the rheologies of
fully viscous mylonites with LBFvv , and IWLvv microstructures. We now modify this theory to derive
a constitutive equation for clastomylonite undergoing FV mylonitic flow (Fig. 1c). In clastomylonite,
the weak phase is assumed, as above, to deform by
dislocation creep (Eq. 2), but the shear strength of
the strong phase (porphyroclasts) is obtained from
the modified Navier–Coulomb criterion for frictional
sliding (Jaeger and Cook, 1979; Streit, 1997):
−s D
1
2
[a C Peff .b
1/] sin.90
arctan ¼d /
(6)
where the effective pressure, Peff D Plith Ppore (respectively the lithostatic
and pore
p
ð fluid pressures), Łand
2
where a D 2−o b and b D .1 C ¼2d /0:5 ¼d .
The coefficient of dynamic friction, ¼d D 0:6, and
the critical shear strength, −o D 50 MPa, are taken
from Byerlee (1978) and are assumed not to vary with
temperature and effective pressure over the range of
depths considered below (Stesky et al., 1974).
Note that in using Eq. 6 to simulate frictional
sliding, we tacitly stipulate a compressive stress state
within the porphyroclasts, such that the effective
pressure Peff is set equal to the effective, intermediate
and least principal stresses, ¦2 D ¦3 . Used together
with the Byerlee (1978) constants, this criterion also
implies that the sliding microfault surfaces within
the porphyroclasts maintain an optimum angle of 30º
to the ¦1 direction in the mylonite. In simple shear,
¦1 is oriented at 45º to the shear zone boundaries and
these microfaults are therefore inclined at a low angle (15º) to the mylonitic foliation. This orientation
is quite reasonable for frictional sliding on ideally irrotational surfaces in clasts at moderate to high shear
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
strains, but obviously does not represent the attitudes
of all rotated sliding surfaces or of purely extensional
cracks at high angles to the mylonitic foliation. For
the sake of simplicity, we will neglect the effect
of unfavourably oriented, rotating sliding surfaces
on porphyroclast strength. This effect is probably
small compared to some of the weakening factors
(pre-existing anisotropies, fluid pressure, subcritical
cracking) discussed below.
To obtain the full expression for the shear strength
of a clastomylonite, one first substitutes Eq. 2 and
the creep parameters of the weak mineral into the
−wr term in Eq. 5 and then substitutes Eq. 6 and the
frictional constants for the strong mineral into the −s
term in Eq. 5. In the resulting new expression, the
shear strength of the bimineralic rock depends not
only on T , Pr , and w , but also on effective pressure
Peff , as expected for a rock containing inclusions that
dilate.
2.3. A criterion for the stability of steady state
microstructures in polyphase rocks
Having derived expressions for all of the mylonitic microstructures depicted in Fig. 1, we now
propose a criterion which allows us to determine the
relative stability of the LBFvv , IWLvv , and IWLfv
microstructures at given values of effective pressure,
temperature, bulk strain rate and volume proportions
of the constituent minerals. We shall assume that
strain energy is minimized in deforming aggregates
and therefore that the most stable microstructure dissipates the least amount of strain energy per unit
time and per unit volume of rock (Handy, 1994a).
The rate of strain energy dissipation for a unit volume of bimineralic rock EP r , is given by the relation EP r D −w Pw w C −s Ps s , where all other terms
have been defined above. In Fig. 2, for example,
EP r is plotted as a function of w for different microstructures and flow mechanisms at given values
of effective pressure, temperature, and bulk strain
rate. The low position of the energy dissipation rate
curve for the IWLfv microstructure on the left-hand
side of the diagram indicates that this microstructure is more stable at low w values, whereas the
IWLvv microstructure predominates at intermediate
and high w values. The LBFvv microstructure yields
higher EP r values and is therefore unstable with re-
179
Fig. 2. Rate of strain energy dissipation of the composite rock
E r , versus volume proportion of weak mineral w . Generic EP r
curves for mylonites with LBFvv , IWLvv , and IWLfv microstructures (see Fig. 1), and for cataclasites undergoing cohesive and
cohesionless frictional sliding. Vertical dashed line delimits low
w range in which mylonite with IWLfv microstructure is energetically stabler from higher w range in which mylonite with
IWLvv , is favoured.
spect to the other two mylonitic microstructures at
all bimineralic compositions. The horizontal curves
for cohesionless and cohesive frictional sliding at
the top of the diagram were calculated with the
Navier–Coulomb relation in Eq. 6 and are therefore
independent of w . Frictional sliding yields the highest EP r values for all w values and so cataclastic
microstructures are less stable than any of the mylonitic microstructures at the hypothetical conditions
of deformation in Fig. 2.
Of course, the use of different material constants
to calculate EP r would change the shapes and relative positions of the curves in Fig. 2 and yield
differently configured microstructural stability fields
(see next section, Fig. 3). Different configurations
would also result if we derived flow laws for bimineralic rocks with three additional microstructures:
(1) weak interconnected layers undergoing frictional flow around stronger, viscous inclusions; (2)
a load-bearing framework undergoing frictional flow
around weak, viscous inclusions; and (3) a load-bearing framework deforming viscously and containing
weaker inclusions that undergo frictional flow. None
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M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
of these microstructures were considered here, partly
because they have never been recognized in naturally deformed rocks (to our knowledge at least),
and also because of the special, possibly transient
conditions that may favour their potential occurrence
in the lithosphere. For example, a frictionally flowing framework containing weak, viscous inclusions
may only exist in rocks that deform at low effective
pressures (i.e., low lithostatic pressures and=or high
pore fluid pressures) and whose inclusions have low
activation enthalpies for creep (e.g., halite inclusions
in anhydrite). Simulating such behaviour lies beyond the scope of this paper and may be considered
sometime later.
We conclude this section by emphasizing that
composite shear strengths obtained with the flow
laws above are only as good as the quality of the
experimentally determined parameters used in these
flow laws. As the use of these parameters in extrapolating flow laws from experimental to natural strain
rates is problematic (Paterson, 1987), the estimates
of mylonitic strength obtained with the equations
above should only be interpreted qualitatively.
3. Applications
3.1. Strength of the lithosphere
The flow laws derived above can be used to calculate lithospheric strength as a function of both depth
and bimineralic composition for mylonites with the
LBFvv , IWLvv , and IWLfv microstructures. Fig. 3a
contains shear strength versus depth profiles for horizontally foliated sections of continental lithosphere
comprising granite (30% quartz, 70% feldspar), gabbro (30% feldspar, 70% clinopyroxene), and lherzolite (50% olivine, 50% pyroxene), all deforming at a
bulk shear strain rate of Pr D 10 12 s 1 , a geothermal gradient of 20ºC=km, and a geobaric gradient
of 27.5 MPa=km. For each of these lithological sections, shear strength versus composition diagrams
calculated for the same Pr , and for given lithostatic
pressures and temperatures are shown in Fig. 3b.
The lithostatic pressures and temperatures for these
diagrams correspond to depths within a hypothetical
lithospheric column that are marked with arrows on
the vertical axes of the adjacent shear strength versus
depth profiles in Fig. 3a. To keep matters relatively
simple, we have assumed zero pore fluid pressure
(see discussion below).
Before we explore the implications of Fig. 3, a
clarifying word about the construction and interpretation of the diagrams is necessary. In Fig. 3a, each
shear strength versus depth profile includes strength
curves for the following flow mechanisms (see caption for material parameters): (1) stable, cohesionless
frictional flow; (2) stable, cohesive frictional flow;
(3) FV mylonitic flow (IWLfv microstructure); and
(4) fully viscous flow for mylonite with an IWLvv
microstructure. The intersections of these strength
curves delimit differently patterned depth intervals
(separated by horizontal, dashed lines) corresponding to domains of different microstructural stability
(see legend in Fig. 3). Within each of these depth
intervals, only one steady-state microstructure is pre-
Fig. 3. Bulk shear strength versus depth profiles (a) and bulk shear strength versus composition diagrams (b) for different bimineral
rocks with LBFvv , IWLvv , and IWLfv microstructures in the continental lithosphere. Dashed lines in (a) and (b) delimit microstructural
stability fields indicated by different patterns (see legend). Solid curves in (a) are shear strength curves for rocks with energetically
stable microstructures, whereas dotted parts of these curves indicate shear strength at conditions for which the same microstructures are
energetically unstable (see text for explanation). Arrows on the vertical axes in (a) indicate depths corresponding to lithostatic pressures
and temperatures in adjacent diagrams in (b), whereas dots in (b) indicate composition and shear strength at the shear strain rate of the
adjacent profiles in (a). Microstructural stability fields in (b) are contoured for shear strength (solid curves) at shear strain rate increments
of a half an order of magnitude. Shear strength contrasts −c , of the minerals at selected bulk shear strain rates are included along the
right-hand vertical axes of the diagrams. Profiles and diagrams constructed with equations discussed in text and the flow laws of Jaoul
et al. (1984) for quartzite (n D 2:4, Q D 163 kJ=m, A D 10 5 MPa-n=s), Shelton and Tullis (1981) for albitic feldspar rock (n D 3:9,
Q D 234 kJ=m, A D 2:51 ð 10 6 MPa-n=s), Boland and Tullis (1986) for clinopyroxenite (n D 3:3, Q D 490 kJ=m, A D 105:17
MPa-n=s), Chopra and Paterson (1981) for dunite (n D 3:35, Q D 444 kJ=m, A D 9:55 ð 103 MPa-n=s), Byerlee (1978) for cohesionless
.¼d D 0:85, −o D 0) and cohesive .¼d D 0:6, −o D 50 MPa) frictional sliding. Conditions assumed: geothermal gradient, T 0 D 20ºC=km,
bulk shear strain rate Pr D 10 12 s 1 , pore fluid pressure is zero, geobaric gradient is 27.5 MPa=km for an average crustal density of 2.8
g=cm3.
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
181
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M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
dicted to be stable, namely, that microstructure with
the lowest rate of strain energy dissipation for the
given conditions of deformation. The strain energy
dissipation rates of the microstructures can be inferred directly from the relative positions of the
shear strength curves in Fig. 3a because bulk shear
strength is proportional to energy dissipation rate
per unit volume of rock at constant bulk strain rate
.−r D EP r =Pr , recall that the profiles in Fig. 3a are
valid for constant shear strain rate and mineral volume proportions). The dotted segments of the shear
strength curves in Fig. 3a indicate the depth intervals over which the microstructures are energetically
unstable (or metastable at low shear strains) according to the stability criterion above. Shear strength
curves for mylonite with the LBFvv microstructure
were not included in Fig. 3a because this microstructure dissipates strain energy at a higher rate and is
therefore energetically unstable with respect to the
other microstructures for the bimineralic compositions and depth range considered here. The criterion of strain energy minimization was also used to
construct the shear strength versus composition diagrams in Fig. 3b. In contrast to the profiles in Fig. 3a,
however, these diagrams show stability fields for the
aforementioned microstructures over the entire range
of bimineralic compositions. In addition, each field
contains bulk shear strength contours for different
values of the bulk shear strain rate Pr . The dashed
boundaries between microstructural stability fields
within the diagrams in Fig. 3b are analogous to the
horizontal dashed lines in Fig. 3a that separate depth
intervals containing different, stable, steady-state microstructures.
The stability fields for the IWLvv , and IWLfv microstructures cover most of the diagrams in Fig. 3b.
The LBFvv field is restricted to a small range of
low w values on the left side of the diagram
for quartz–feldspar and olivine–pyroxene rocks, and
is not present at all in the diagram for feldspar–
pyroxene rock (insets of diagrams in Fig. 3b). In
general, the IWLfv , microstructure is favoured at
high bulk strain rates and=or low temperatures, corresponding to high mineral strength contrasts. The
asymmetrical, concave shape of the strength contours in both IWL stability fields indicates that rock
strength is most dependent on bimineralic composition at low w values. Thus, only a modest amount of
weak mineral in interconnected layers parallel to the
shearing plane suffices to reduce the bulk strength of
the rock to levels approaching that of the pure weak
mineral.
The pressure-dependence of FV flow in clastomylonite (IWLfv microstructure) increases nonlinearly with decreasing temperature (Fig. 4a) and
with increasing volume proportion of porphyroclasts
(Fig. 4b). At high temperatures and=or high volume
proportions of interconnected weak phase, the T and
Fig. 4. Pressure dependence of FV mylonitic flow in quartz–feldspar clastomylonite: (a) shear strength versus lithostatic pressure diagram
with shear strength curves for different temperatures T , at constant shear strain rate .Pr D 10 12 s 1 ) and volume proportion of weak
phase .w D 0:3 quartz); (b) shear strength versus lithostatic pressure diagram with shear strength curves for different volume proportions
w quartz, at constant Pr (10 12 s 1 ) and T (350ºC).
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
w contours are nearly flat (Fig. 4), indicating that
the temperature-dependence of FV mylonitic flow is
similar to that of fully viscous mylonitic flow in an
IWLvv microstructure.
In the shear strength versus depth profiles in
Fig. 3a, the IWLfv microstructure is stable over a
relatively narrow depth interval between frictional
flow in the upper crust and fully viscous flow at
greater depths. We found that this prediction holds
for any combination of experimental monomineralic
flow laws currently available in the literature for the
minerals making up the bimineralic rock. In nature,
however, the actual depth range of FV mylonitic flow
is probably much larger due to several phenomena
that, acting individually or in concert, can weaken
the porphyroclasts:
(1) Pressurized metamorphic fluids reduce effective pressure and, in triaxial rock deformation experiments, have been shown to decrease rock strength
and induce fracture (e.g., Handin et al., 1963; Murrel, 1965; Paterson, 1978). Healed syn-mylonitic
microveins containing hydrous minerals within competent inclusions (Fig. 5) are testimony to fracturing
in the presence of pressurized fluids in high-grade
shear zones. The feldspar inclusions in Fig. 5 are
elongate and show no evidence (e.g, asymmetrical
tails, arcuate inclusion trails) of having rotated in the
surrounding matrix during mylonitic deformation.
Therefore, the moderate angle of these microveins
with respect to the mylonitic foliation (Fig. 5) is
probably primary and suggests that they initiated
oblique to the shearing plane as purely extensional
or as hybrid extensional-shear fractures, possibly
along pre-existing twinning planes. This vein geometry also indicates that fluid pressures were close
to the magnitude of the minimum principal stress
and that the differential stresses in the porphyroclast
were smaller than those required for compressional
shear failure (Secor, 1965; Sibson, 1981; Etheridge,
1983).
(2) Subcritical crack growth within porphyroclasts
can lead to a significant reduction in their long-term
strength (Atkinson and Meridith, 1987). This type of
crack propagation is associated with enhanced ionization and reaction rates in stressed regions around
crack tips, leading to slow, stable growth of fractures
at relatively low, local stress concentrations. Mitra
(1984) inferred subcritical cracking from the termi-
183
nation of cracks at the clast-matrix interface and
from the preservation of crack tips in clasts within
mylonites (see his fig. 5). Existing experimental
data indicate that subcritical crack growth is likely
to occur over a broad range of temperatures, pressures, and fluid activities (Atkinson, 1984; Atkinson
and Meridith, 1987). Unfortunately, subcritical crack
propagation is still poorly understood and the limited
data in the literature do not allow one to quantify its
weakening effect on clastomylonites.
(3) Anisotropies within porphyroclasts (e.g., preexisting fractures, cleavage or twinning planes) represent potential planes of weakness which, if oriented at low to moderate angles to the local direction of maximum principal stress ¦1 , can be easily
activated as sliding surfaces. Any of these effects
would be expected to extend the depth range of FV
mylonitic flow downwards at the expense of fully
viscous flow.
To explore the weakening effect of pore fluid on
the transition from frictional flow to FV mylonitic
flow, we consider three end-member cases, corresponding to the three crustal strength curves for
granitic rock (30% quartz, 70% feldspar) in Fig. 6.
Case 1 is the reference state used in Figs. 3 and 4
above in which Byerlee’s (1978) frictional constants
for cohesionless .¼d D 0:85/ and cohesive .−o D 50
MPa, ¼d D 0:6/ frictional sliding are applied and
the pore fluid factor, ½v (D Ppore =Plith ) is assumed to
be zero. In case 2, we again use Byerlee’s frictional
constants, but assume that near-lithostatic fluid pressures .½v D 0:9/ prevail during cohesive frictional
sliding at depths exceeding several kilometres. This
is qualitatively consistent with the inferred build-up
of supra-hydrostatic fluid pressures in shallow to intermediate parts of faults at several kilometres depth
(Sibson, 1994; Streit, 1997). Streit and Cox (1998)
have also shown that near-lithostatic fluid pressures
existed at least transiently during mylonitization in
some greenschist facies granitoid shear zones. Case
3 incorporates near lithostatic fluid pressure and a
frictional coefficient of 0.6, but uses an average laboratory value of the cohesive shear strength .−o D 20
MPa) for intact granites and gneisses (Handin, 1966)
at elevated pressure instead of Byerlee’s best-fit
value of 50 MPa for a broad range of rock types.
Stesky et al. (1974) have shown that a frictional
coefficient of about 0.6 is valid for most basement
184
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
Fig. 5. (a) Mylonite with an IWL structure comprising competent inclusions of partly dynamically recrystallized, anorthitic feldspar in
a weak matrix of dynamically recrystallized hornblende and brittly deformed clinopyroxene. Arrow within feldspar inclusion points to
microvein shown in (b) (photo length 105 mm). (b) Close-up of partly healed, hornblende-filled microvein (arrow) in feldspar inclusion
(see text for explanation). Narrowly spaced fractures offsetting this microvein formed during post-mylonitic cataclasis and are not
relevant to this paper. Photo length 0.95 mm, sample Iv-850 from the Cannobina valley in the Ivrea–Verbano zone, northern Italy. Both
pictures taken with crossed nichols. Thin section cut parallel to X Z fabric plane.
rocks at temperatures and normal stresses up to
600ºC and 600 MPa, respectively.
Fig. 6 shows that at high fluid pressure .½v D
0:9/, FV mylonitic flow occurs within a somewhat
broader depth range and at greater depths than in
the absence of fluid pressure (compare curve 1 with
curves 2 and 3, Fig. 6). Also at high fluid pressure,
the transition between cohesive frictional sliding or
fracturing of intact rock and FV mylonitic flow is
shifted to lower depths. Not surprisingly, case 3
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
185
seismogenic zone inferred for active faults at high
fluid pressures (Streit, 1997) and falls within the
range of flow stresses obtained independently from
quartz palaeopiezometry in many crustal mylonite
zones (shaded box in Fig. 6). This is consistent
with the idea that brittle deformation within and
immediately above the depth level for FV mylonitic
flow occurs at transiently high pore fluid pressures
.½v D 0:9/. Substituting yet higher values of ½v
and=or lower values of ¼d into Eq. 6 in the flow law
for clastomylonite dramatically extends the depth
range of FV mylonitic flow and lowers the depth of
the transition from cohesive frictional sliding to FV
mylonitic flow.
3.2. Strength of natural mylonite
Fig. 6. Shear strength versus depth curves for granitic crust
(30% quartz, 70% feldspar). Only energetically stable parts of
the shear strength curves are shown. Numbers 1 to 3 refer
to end-member cases incorporating different pore fluid factors
and frictional constants in Eq. 6 for cohesive frictional sliding
and for frictional flow of the porphyroclasts in clastomylonite,
as discussed in text. Shaded horizontal bars indicate predicted
depth range of FV mylonitic flow for each of these three cases.
Rectangular patterned field represents range of flow stresses
obtained from palaeopiezometry on dynamically recrystallized
grains and subgrains of quartz in mylonite zones originating
at different depths and temperatures (Kohlstedt and Weathers,
1980; Etheridge and Wilkie, 1981; Ord and Christie, 1984).
Shear strength curves constructed with equations discussed in
text and the flow laws of Jaoul et al. (1984) for quartzite,
Shelton and Tullis (1981) for albitic feldspar rock, and Byerlee’s
(1978) constants for cohesionless and cohesive frictional sliding
(parameters listed in caption to Fig. 3).
yields the lowest crustal shear strengths (curve 3 in
Fig. 6). The estimated peak strength of about 80 MPa
at the transition between cohesive frictional sliding
and FV mylonitic flow for thrusting in case 3 is
similar to the peak shear strength at the base of the
The bimineralic flow laws presented above can
also be used to constrain the bulk strength of natural
mylonites. To do this, one needs to know the range of
temperatures and strain rates of deformation, and the
volume proportions of the two minerals that accommodated most of the strain in the mylonite. Also, the
mylonitic microstructure observed in nature should
match one of the three, aforementioned model structures. Provided the minerals in the natural mylonite
show evidence of deformation mainly by dislocation
creep (in the matrix and=or clasts) or cataclasis (in
the clasts), one can then estimate a range of bulk
shear strengths.
For example, the quartz–feldspar clastomylonite
in Fig. 7 contains feldspar clasts and interconnected
layers of dynamically recrystallized quartz that define the mylonitic foliation. Quartz is inferred to have
been the weaker phase at the time of deformation
because it underwent dynamic recrystallization and
because the feldspar clasts are fractured (Fig. 7a).
The conditions of deformation are estimated to have
been T D 350 to 400ºC, P D 480 to 550 MPa at
shear strain rates ranging from 10 11 to 10 13 s 1
(Handy, 1987). We traced the boundaries between
quartz and feldspar in the sample from a thin section
photo onto paper and then made a black-and-white
image of this tracing (Fig. 7b). We then estimated
the areal proportions of quartz and feldspar from the
image with a surface-integrating graphic program
(NIH-Image 1.6). In equating areal proportions with
volume proportions of quartz and feldspar in the
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M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
Fig. 7. (a) Micrograph of a greenschist facies, granitoid clastomylonite containing 28 vol.% quartz and 72 vol.% feldspar. (b)
Black-and-white image of the mylonite shown in (a) used to calculate areal proportions (see text for explanation); q D quartz, f D
feldspar. Photo length is 3 cm, sample number HD-47.
sample, we neglected the slicing or truncation effect
(e.g., Exner, 1972). This is justified in light of the
complicated phase geometries and probably results
in only a slight underestimate of the actual volume
proportions of feldspar in the rock.
Depending on the assumed shear strain rate, the
shear strength of the quartz–feldspar clastomylonite
is predicted to have ranged from 220 to 515 MPa
for T D 350ºC and 420 to 475 MPa for T D 400ºC
(Fig. 8). These values are about 2 to 20 times higher
than flow stress estimates for quartzite mylonites
(20–150 MPa) obtained with dynamically recrystallized grain-size palaeopiezometers (Etheridge and
Wilkie, 1981). This discrepancy may be insignifi-
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
Fig. 8. Shear strength versus bimineralic composition diagrams
with shear strength contours (thick lines) and isopleths (thin
lines) for the greenschist facies, granitoid clastomylonite described in the text and depicted in Fig. 7. Arrows indicate range
of estimated shear strengths. Thick dashed line in lower diagram delimits IWLfv and IWLvv stability fields. Experimental
flow parameters for quartz and feldspar as in Fig. 3. Diagrams
constructed with equations discussed in text and the flow laws
of Jaoul et al. (1984) for quartzite, Shelton and Tullis (1981)
for albitic feldspar rock, and the constants of Byerlee (1978) for
cohesive frictional sliding (material parameters listed in caption
to Fig. 3).
187
estimates for quartz–feldspar mylonite are reasonable, insomuch as feldspathic aggregates have higher
laboratory strengths than quartzite at the same temperature (Carter and Tsenn, 1987; Kohlstedt et al.,
1995) and feldspar clasts in quartz–feldspar mylonite
are known to concentrate stress in the interconnected
quartz layers (Handy, 1990). Our relatively higher
strength estimate compared to that for mylonitic
quartzite is also qualitatively consistent with the
finding of Hansen and Carter (1982) that the creep
exponent and activation energy of power law creep
for dry granite is higher than that for quartzite at the
same laboratory conditions of deformation. Unfortunately, a better test of our method for estimating
the strength of clastomylonites is not yet possible,
because there are currently no published experimental flow laws for a bimineralic rock and its two
constituent minerals, all determined at the same conditions of temperature, strain rate, confining pressure
and pore fluid pressure.
We point out that the method above for estimating bulk strength should really only be applied to
mylonitic rocks in which there is no microstructural evidence of significant diffusive mass transfer between the mineral phases that accommodate
most of the deformation (e.g., during pressure-solution creep or diffusion-accommodated grain-boundary sliding). Diffusive mass transfer mechanisms
are strongly grain-size-sensitive, relax intragranular
stresses (White, 1976) and are usually associated
with changes in the volume proportions of the constituent phases (Wheeler, 1987). The latter condition
violates the basic assumption made in the approach
above that the volume proportions of both phases do
not vary with strain. Generally, grain-size-sensitive
creep mechanisms are associated with lower viscous strengths than grain-size-insensitive, power law
creep. Therefore, if our method were applied to rocks
in which diffusive massive transfer in the matrix
was the dominant, strain-accommodating process, it
would probably overestimate the actual strength of
the rock.
4. Discussion and conclusions
cant given the many analytical and theoretical uncertainties of both our method and the grain-size
palaeopiezometers. Nevertheless, the higher strength
Consideration of combined frictional and viscous
rheologies in mylonite has several implications, first
188
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
for the terminology of fault rocks and deformational
processes, and second for the rheological interpretation of natural fault rocks at the transition from
frictional to viscous deformation in the lithosphere.
Our model of bimineralic, FV mylonitic flow indicates that the rheology of clastomylonites is strongly
dependent on temperature, strain rate, and mineral
volume proportion, with only a modest pressure sensitivity due to brittle, dilatational deformation of
the porphyroclasts. Even small amounts of a weak
mineral .w < 0:1) suffice for the weak mineral to
govern the rheology of the whole rock. This is intuitively reasonable in light of the observation that
most of the strain in mylonites with an IWL microstructure is accommodated within a weak mineral
undergoing dynamic recrystallization and=or diffusion-accommodated grain-boundary sliding (Handy,
1990). Thus, the widespread use of the term ‘semibrittle’ to describe the rheology both of clastomylonites and of cataclastic fault rocks undergoing
adhesive wear (e.g., Scholz, 1988) is somewhat
misleading from a mechanistic standpoint, as the
behaviour of clastomylonites is predominantly nonlinear viscous.
The prediction above that shear strength within
the depth range of FV mylonitic flow decreases with
increasing depth and temperature (Fig. 3) is only
partly consistent with Scholz’s synoptic model of
strength and microstructure within the transitional
domain between fully frictional sliding (abrasive
wear) at shallow depths and fully viscous flow deep
in the crust (Scholz, 1988, 1990). Scholz (1988) argues that adhesive wear mechanisms (e.g., intracrystalline plasticity in asperities on fault surfaces) can
engender mylonitic fabrics and microstructure, even
though the overall behaviour of the fault rock is frictional. In his concept, the presence of mylonitic fault
rock at depth signifies the temperature-dependent
onset of intracrystalline plasticity (see his fig. 4). We
propose that the onset of intracrystalline plasticity in
quartz does not correspond with the development of
mylonite, because at low temperatures such plasticity
involves dislocation glide on an insufficient number
of slip systems (usually only one or two) to accommodate large strains compatibly. This is expected to
lead to work-hardening followed by brittle failure
and cataclasis after only small strains. Schmid and
Handy (1990) point out that two conditions are nec-
essary for mylonite to form: (1) Thermally activated
dislocation climb must be possible in at least one of
the minerals of the rock to prevent that phase from
hardening and to allow this phase to accommodate
large strains by undergoing dynamic recovery and
recrystallization. Deformation studies in both naturally and experimentally deformed, polycrystalline
quartzite indicate that relatively small strains ( < 1,
e < 10%) suffice to initiate dynamic recovery and
recrystallization (e.g., ; White, 1976, 1979; Weathers
et al., 1979; Dell’Angelo and Tullis, 1989; Hirth and
Tullis, 1992). (2) The weak phase must form interconnected layers subparallel to the shearing plane,
i.e., the rock must have an IWL microstructure. Reviewing the literature on experimentally deformed
two-phase materials, Handy (1994a) cites coaxial
strains of about 10–30% for the brittle breakdown of
an LBF microstructure to form an IWL microstructure. Both of these conditions are fulfilled only after
a critical amount of strain has accrued. It follows
that the transition from cataclastic to mylonitic deformation, as well as the depth of the shear strength
maximum within the lithosphere are strain- and composition-dependent features.
The generic strength versus depth profiles for
granitic crust in Fig. 9 summarize some new and
modified notions on crustal rheology stemming from
our study of combined frictional and viscous rheologies in clastomylonite. The most obvious modification is that FV mylonitic flow occupies a depth interval between cohesive frictional flow involving adhesive wear and fully viscous mylonitic flow (compare
configurations A and B in Fig. 9). In all rocks (except those with very small w values), the crustal
strength maximum is expected to coincide with the
upper depth limit of FV mylonitic flow (see also Sibson, 1983, his fig. 2). This is where temperatures are
sufficiently high to facilitate dislocation creep (i.e.,
dislocation glide-plus-climb) in the weakest mineral of the rock, enabling an IWLfv microstructure
to form with schistosity subparallel to the shearing
plane. The value of the strength maximum at the
intersection of the strength curves for cohesive frictional flow and FV mylonitic flow is less than that
obtained if one were only to consider a direct change
from cohesive frictional flow to fully viscous flow
in mylonite with an IWLvv , microstructure (compare
peak strengths for configurations A and B in Fig. 9).
M.R. Handy et al. / Tectonophysics 303 (1999) 175–191
Fig. 9. Synoptic shear strength versus depth profile through
granitic crust showing relationship between crustal strength, type
of steady-state flow and microstructure, and dominant deformation mechanisms (see text for discussion). Patterned depth
intervals are same as in Fig. 3. Three configurations of strength
curves depicting strength maxima for the following mechanistic
and microstructural transitions (see text): A D direct transition
from cohesive frictional flow to fully viscous mylonitic flow with
an IWLvv microstructure; B D transition from cohesive frictional
flow to FV mylonitic flow at zero pore fluid pressure; C D
transition as in B but at high pore fluid pressure.
High pore fluid pressures considered in the previous
section .½v D 0:9, Fig. 6) expand the depth range
of FV mylonitic flow, and both decrease and depress
the crustal strength maximum (and with it, the upper depth limit of mylonitization) to greater depths
(compare configurations B and C in Fig. 9).
Although cataclastic flow mechanisms have been
treated only summarily in this paper, we included
bulk shear strength curves in Fig. 9 for stable
frictional flow in the upper crust. The kink in the
strength curve for frictional flow marks changes in
the values of cohesion, −o , and frictional coefficient,
¼d , on active faults. These changes may be related to
the onset of one or more creep processes (e.g., pressure-solution, dislocation glide, Stesky et al., 1974)
that also cement fragments and=or weld asperities on
sliding surfaces. Thus, our model accounts at least in
principle for fault compaction and lithification which
can lead to the build-up of near-lithostatic pore fluid
pressures. Such pore fluid pressures can significantly
reduce frictional fault strength, as recently modelled
by Streit (1997). The consideration of near-lithostatic
pore fluid pressures (configuration 3 in Fig. 9) allows
189
us to predict peak flow strengths for bimineralic
rocks that are comparable to flow stress estimates
from quartz grain-size palaeopiezometers applied to
natural quartz-rich mylonites.
As mentioned in previous work (Handy, 1994a),
deformation mechanisms other than dislocation
creep and frictional sliding (e.g., granular flow
accommodated by diffusion and=or by the syntectonic nucleation and growth of new mineral phases,
Stünitz and FitzGerald, 1993) are associated with
different composite flow laws than the ones employed in this paper (Fueten and Robin, 1992;
Wheeler, 1992). Characterizing and modelling such
deformational processes will modify the view of
lithospheric rheology presented here, particularly as
regards rocks that deform at or near the limits of
their mineralogical stability.
Acknowledgements
We thank Claudio Rosenberg, Andreas Schlaefke,
Susanne Palm and Peter Bauer for discussions. G.
Mitra and especially S.M. Schmid provided critical
reviews that helped us avoid semantic pitfalls and
clarified our presentation and argumentation. The
computer program used to calculate Figs. 3, 4, 6
and 8 was written in Mathematica 2.2TM by S. Wissing as part of her diploma thesis. Copies of this
program are available on request from the first two
authors. The support of the Deutsche Forschungsgemeinschaft in the form of DFG- Grant Ha 2403=1-1
is acknowledged with gratitude.
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